Q: This plant popped up (and how!) and is still growing. What in the world is it?
A: In a “Biggest Leaf” contest, the prize almost always goes to Princess tree (Paulownia tomentosa). It has huge leaves, especially on young plants or on stumps that have resprouted.
A paulownia leaf has no lobes and looks like a big green heart.
I do not recommend paulownia as a landscape tree because the limbs are so brittle and prone to breaking. Most folks consider it a weed.
The purple flowers in spring are attractive, like upside-down wisteria, but they produce a multitude of nuts that sprout in every crack and crevice in your landscape.
Paulownia (Princess Tree)